Xenakis's screens theory distributes grains on time-frequency planes using stochastic processes

Xenakis proposed a formal theory of granular synthesis based on screens - snapshots of grain distributions on a time-frequency grid (the plane of frequency versus intensity). Each screen defines the statistical distribution of grains over a short time interval. A composition consists of a sequence of screens, with transitions between them governed by Markov chain probabilities. The ataxy parameter (from 0=complete order to 1=complete disorder) controls the regularity of the distribution within each screen. Xenakis derived the theory from statistical mechanics (Maxwell-Boltzmann distributions), treating the granular cloud as an acoustic gas.

Examples

A screen might specify: 80% of grains uniformly distributed between 200-400 Hz, 20% randomly scattered across 400-2000 Hz. The next screen shifts the distribution with specified transition probabilities.

Assessment

What is a screen in Xenakis’s granular synthesis theory? How does the ataxy parameter relate to the perceived texture of a granular cloud?